pmodes

Pmodes, short for pressure modes, are a class of stellar oscillations in which pressure acts as the restoring force. They manifest as standing acoustic waves within a star, most prominently observed in the Sun and other solar-like stars. Pmodes probe the outer to mid layers of a star and are trapped between the photosphere and an interior turning point, where the wave propagation transitions.

These modes are described by oscillation quantum-like numbers: radial order n, angular degree l, and azimuthal order m. They have relatively high frequencies, typically in the milli-Hertz range for the Sun. The radial structure becomes more complex with higher n, and larger l yields more horizontal flow patterns. The frequencies tend to cluster into a regular pattern, with the large frequency separation Δν being roughly proportional to the square root of the star’s mean density, and smaller separations δν providing information about the stellar core.

Observationally, pmodes are detected as periodic Doppler shifts or brightness variations at the stellar surface. In helioseismology and asteroseismology, instruments measure these surface signals to infer internal properties such as sound speed, density, and rotation. Pmodes have been central to constructing detailed models of the Sun and to characterizing the internal structure of other stars, including their age and evolutionary state.

Pmodes complement other oscillation classes, such as g-modes, where buoyancy is the restoring force, and f-modes, which are surface gravity waves. While p-modes dominate in Sun-like stars and are relatively easier to detect, g-modes provide deeper-core information in some cases.